Does financial integration impact performance of equity anomalies?

Sharma, Gagan; Sehgal, Sanjay; Mishra, Anil V. Article Does financial integration impact performance of equity anomalies? Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Sharma, Gagan; Sehgal, Sanjay; Mishra, Anil V. (2022) : Does financial integration impact performance of equity anomalies?, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 10, Iss. 1, pp. 1-51, https://doi.org/10.1080/23322039.2022.2111802 This Version is available at: https://hdl.handle.net/10419/303757 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Cogent Economics & Finance ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/oaef20 Does financial integration impact performance of equity anomalies? Gagan Sharma, Sanjay Sehgal & Anil V. Mishra To cite this article: Gagan Sharma, Sanjay Sehgal & Anil V. Mishra (2022) Does financial integration impact performance of equity anomalies?, Cogent Economics & Finance, 10:1, 2111802, DOI: 10.1080/23322039.2022.2111802 To link to this article: https://doi.org/10.1080/23322039.2022.2111802 © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Published online: 25 Aug 2022. Submit your article to this journal Article views: 935 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 FINANCIAL ECONOMICS | RESEARCH ARTICLE Does financial integration impact performance of equity anomalies? Gagan Sharma 1 , Sanjay Sehgal 2 and Anil V. Mishra 3 * Abstract: We examine prominent market anomalies and evaluate the efficacy of alternative asset pricing models under different financial integration settings. A financial integration index is developed for classifying 25 sample markets into high-, mediumand low integration groups. Size is found to be the strongest anomaly in world markets, followed by value and liquidity. Value and profitability effects are larger for low-integrated markets. Highly integrated markets experience short-term momentum while many low-integrated markets exhibit mild reversals. Fama and French five-factor model outperforms capita l asset pricing model (CAPM) and Fama and French three-factor model in explaining returns. International factors augment the role of local factors for more integrated markets. Our study has implications for global investors to design anomaly based investment strategies. Subjects: International Finance; Corporate Finance; Investment & Securities Keywords: financial integration index; asset pricing anomalies; factor models 1. Introduction Financial markets have become increasingly integrated over the past few decades (Ayuso & Blanco, 2001; Hoffmann et al., 2019). This can be attributed to globalisation and rising foreign investment leading to greater capital and information flows. Various events like the “Asian crisis”, dot-com bubble, asset pricing boom leading up to the global financial crisis, “quantitative easing” along with subsequent “tapering”, have demonstrated that financial integration between the markets can lead to global events impacting local asset prices. Past studies have primarily focused on asset pricing tests in developed and emerging market settings based on Morgan Stanleys (MSCI) classification 1 of world markets which derives on three broad criteria of economic development, market accessibility, and size-liquidity conditions. However, this classification doesnt offer the required distinction between economic and financial integration across markets for a global investor. Some developed markets may be less financially integrated, whereas few emerging markets may exhibit a higher level of financial connectedness. So classifying the markets, with a reasonable degree of breadth and depth, on the basis of financial integration, could hold greater relevance for global investors (see Akbari, Ng and Solnik, 2020; Bekaert et al., 2013). MSCI emerging market classification offers no distinction for vastly different markets like China or India as against Qatar or the Czech Republic in terms of breadth and depth. Investors can benefit from developedto-emerging markets diversification, and inter-regional diversification like EU-to-Asia or US-to-Asia as regional integration is relatively more robust than global integration (Sehgal et al., 2019). “Developed” and “emerging” market classifications are attributes of economies, but financial markets in these economic groupings may be heterogeneously integrated. An investor from a highly integrated developed financial market could prefer to diversify into another mature market that is relatively less integrated to the global market. Similarly, this investor may not be Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 1 of 51 Received: 19 January 2022 Accepted: 06 August 2022 *Corresponding author: Anil V. Mishra, School of Business, Western Sydney University, Australia E-mail: a.mishra@westernsydney. edu.au Reviewing editor: David McMillan, University of Stirling, Stirling UK Additional information is available at the end of the article © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. adequately diversified if the asset allocation is made to an emerging market that is almost as integrated into the global market as her local financial market. Thus, for global investors who seek superior risk-adjusted returns through international diversification, financial integration can provide an alternative approach for categorising markets, in addition to the “mature” and “emerging” market classification. 2. Financial integration and equity market anomalies Capital markets are said to be integrated if they offer identical rewards to investors for a similar level of risk (Bekaert & Harvey, 1995). So closely integrated set of markets should offer similar compensation for investment risks related to size, value, prior returns, or liquidity-based investing. Financial markets that are highly integrated with the global market, with a large investor base, should be informationally more efficient and exhibit smaller anomaly 2 premiums if anomalies are seen as a sign of inefficiency. Similarly, less integrated markets, being more segmented, should offer different compensations for similar levels of risk. The anomaly premiums could be higher in less financially integrated markets due to absence of mature global investors. So equity premiums in low-integrated markets could vary significantly from those observed in more integrated markets. Hence, we can hypothesize that anomaly premium should be different for high integration group (HIG) and low integration group (LIG) markets. The differences in behaviour of anomalies at high and low levels of financial integration could also be in terms of strength, i.e., anomalies may be stronger or weaker for different integration group markets. The difference in nature of anomaly premiums might just not be restricted to their relative size. The anomaly premiums also be directionally different. It is possible that less integrated markets, will be more segmented and are likely to have absence of sophisticated global investors resulting in higher volatility, lower levels of liquidity and highly sentiment driven. Studies have found that less mature markets are more prone to overreaction (Ahmad & Hussain, 2001; Wu, 2011). Markets with participants prone to underreaction could exhibit momentum effect while contrarian effect might prevail in markets where investor overreaction dominates. In addition, anomalies like the asset growth effect are dependent on the nature of the domestic credit system, and markets may register negative investment premiums 3 . Hence there are strong possibilities of anomaly premiums varying with the level of financial integration and this issue could be empirically explored. Further, domestic returns in highly integrated markets could be better explained by the world factors due to their greater openness than low-integrated markets. However, local factors could still play a dominant role in explaining the variance of their portfolio returns, possibly due to a large domestic investor base and persistence of home bias. Home bias can persist even at high levels of integration as marginal benefits could be lower than marginal costs of diversification Levy and Levy (2014) Thus, the impact of global events on domestic asset prices should vary with the strength of financial integration between a domestic and global market. Therefore, we hypothesize that world factors should better explain the high integration market portfolio returns than low integration market portfolio returns. Finally, the comparative success of single-factor versus multifactor models, using local and global factors in explaining domestic returns under varied financial integration settings warrants further examination. Financial integration should hold strong relevance for the global investors, in addition to the traditional classification of “developed” and “emerging” markets. Previous studies have examined anomalies in international markets but not from an integration point of view. Fama and French (2012, 2017) analyse the size, value, and momentum in stock returns for North America, Europe, Japan, and the Asia Pacific regions. Our study also includes the emerging markets and explores the variation in anomaly premiums under different integration settings. Hollstein (2021b) evaluates the performance of global, regional, and local models in explaining a large set of cross-sectional anomalies. Hollstein (2021b) observes that global and regional factor models create substantially Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 2 of 51 larger average absolute alphas than local factor models, thus creating possibilities for international diversification of anomaly strategies. Jacobs and Müller (2020) study the preand post-publication return predictability of several cross-sectional anomalies in a range of financial markets and find evidence of anomaly premiums which they attribute to mispricing resulting from market segmentation. Jacobs and Müller (2020) also suggest further investigation into the existence of crosscountry variation in anomaly profitability. Hou et al. (2011) identify the characteristics and associated factor portfolios like momentum and cashflow-to-price ratio that offer the highest explanatory power for global stock returns but also acknowledge to not considering some key firm-level characteristics such as liquidity and asset growth, which our study includes. As empirical literature is fairly silent on the relationship between financial integration and asset pricing anomalies, we explore this issue in our study. Against this background, the relationship between financial integration and equity market anomalies is studied, and the role of local and global factor models is evaluated in integration settings. We specifically study the performance of anomalies for the group of markets classified on the basis of financial integration to find evidence of significant differences in the anomaly premiums for integration-based groups. Then, we evaluate the performance of local, world and hybrid models but for the three financial integration-based classifications of sample markets. Our study differs from previous studies as it focuses on examining market anomalies for different financial integration segments. Traditionally, financial integration has been measured by the size of financial flows from a market to the rest of the world and vice-versa (Lane & Milesi-Ferretti, 2003). In this study, we develop an alternative measure of financial integration based on information transmission between the sample markets. Our financial integration (FI) index is then used to classify markets into “high”, “medium” and “low” integration groups. This approach differs from traditional market classification into “developed”, “emerging” and “frontier” groups. Using the new FI index-based classification, this study attempts to address two research issues. Firstly, we study the behaviour of prominent stock market anomalies for each of the three integration groups. Secondly, we examine the performance of local and global factors using single and multifactor models in explaining the cross-section of stock returns. We use the single-factor model capital asset pricing model (CAPM) and multifactor models, Fama and French (1992) and Fama & French, 2015), their world factor equivalents, and hybrid models, which combine local and foreign factors. We specifically examine six market anomalies i.e. size, value, liquidity, prior returns, profitability and asset growth. In addition, we further evaluate the role of single-factor and multifactor pricing models (both local and global variants) in explaining returns. Past studies have analysed the performance of local and global factors in explaining domestic returns. Although prior studies (Griffin, 2002) have analysed how the global factors augment local factors in explaining the portfolio returns, we explore the role of global factors additionally in the context of financial integration. This linkage between integration and the role of global factors was missing in earlier strands of literature, to the best of our knowledge This study attempts to answer the following research questions: Do market anomalies behave differently under alternative financial integration settings? Do anomaly premiums differ for LIG and HIG markets? Do multifactor factors models outperform single-factor CAPM in explaining the cross-section of returns for global markets? Do foreign factors play a more important role in explaining returns for high integrated markets? We find size effect to be the strongest anomaly in global equity markets with a mean monthly premium of 2.16%. World value and liquidity premiums are 1.35% and 0.58% per month. The global prior returns and profitability premiums are relatively small. Investment effect is weak and negative, implying that high investment companies can outperform low investment companies across several markets. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 3 of 51 Financial integration doesnt seem to impact size, liquidity and investment effects as there is not much difference in the premia for highand low-integrated markets. However, the value and profitability effect are much stronger for less integrated markets when compared to highly integrated markets. Further, markets with higher integration exhibit momentum, while lowintegrated markets experience mild reversals in returns. Evaluating the power of single and multifactor asset pricing models, we find that Fama-French five-factor model is a better predictor of returns than one factor CAPM and Fama-French three-factor model. Local factor-based models are suitable for less integrated markets while hybrid factor models, comprising local and foreign factors, do a better job for more integrated markets. Our findings confirm that the performance of some of the market anomalies and asset pricing benchmarks vary for markets with different levels of financial integration. We perform a few robustness tests to support our work. This study contributes to the literature by developing an alternative financial integration index, examining key equity market anomalies, and evaluating the performances of factor models for different financial integration group markets. Our findings add to the discussion on financial market integration and equity anomalies. Section 2 provides a brief literature review related to financial market anomalies and also literature related to local, foreign and world factors. In Section 3, we describe data and their sources. The methodology for developing the financial integration index, portfolio formation and construction of risk factors are discussed in Section 4. Section 5 evaluates the performance of six prominent equity market anomalies for cross-section of markets and discusses the role of local and global risk factors in explaining the portfolio returns under different financial integration settings. Robustness tests are discussed in Section 6, while the final section includes the concluding remarks on the findings from the study. 3. Literature review 3.1. Literature review—market anomalies We examine six major equity market anomalies, namely, size, value, momentum, liquidity, profitability and investment, for a wide range of global markets. In empirical literature “size” anomaly is seen when smaller size firms provide superior risk adjusted returns in comparison with larger firms (Banz, 1981). It may result from presence of transaction costs (Stoll & Whaley, 1983), infrequent trading (Roll, 1981), illiquidity (Amihud & Mendelson, 1986), business cycles (Chan et al., 1985), different risk and return characteristics (Chan & Chen, 1991), prevalence of micro stocks (Fama & French, 2008). van Dijk (2011) finds evidence of size effect across the global markets. Few studies find that size effect has weakened for some markets or it has become insignificant (Crain, 2011; Schwert, 2003). Dimson et al. (2017) find the magnitude of small cap premium to be quite modest across global markets. Alquist et al. (2018) advocate size effect to be mere “fiction”. The outperformance of value stocks over growth stocks on a risk-adjusted basis in empirical asset pricing is called the value anomaly. It has been attributed to various causes like risk (Fama & French, 1992, 1996) and overreaction (De Bondt & Thaler, 1987; Lakonishok et al., 1994). Barberis et al. (1998) in their study on investor sentiment attribute the value effect to overreaction by investors to bad news. Fama and French (2012) report the presence of value effect in their study of developed markets from North America, Europe, Asia-Pacific and Japan. Cakici et al. (2013) in their study of 18 emerging stock markets, from 1990 to 2011, find strong evidence of value effect in the prediction of asset returns. Alquist et al. (2018) see value effect as a prominent factor in comparison with size effect. In the “momentum” anomaly, over an intermediate time horizon, the past outperformers (high return stocks) continue to be future outperformers, and previous period losers (low return stocks) remain future underperformers (Jegadeesh & Titman, 1993). Momentum anomaly has been attributed to various factors like sectoral returns (Liu & Zhang, 2008; Moskowitz & Grinblatt, Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 4 of 51 1999), past trading volume (Lee & Swaminathan, 2000), investor biases in their processing of information (Barberis et al., 1998), macro-economic variables (Chordia & Shivakumar, 2002) and positive earnings surprises (Novy-Marx, 2015). Several mature and emerging markets have been studied in empirical literature and momentum and contrarian anomalies have been identified in various mature and emerging markets (Antoniou et al., 2007; Chui et al., 2010; Hanauer & Lauterbach, 2019; Rouwenhorst, 1998; Vu, 2012) When less liquid (low volume) stocks offer higher returns over more liquid (higher volume) stocks, it is characterized as a liquidity anomaly. Returns have been found to have a negative relationship with liquidity as the investors have to be compensated for the risk of holding stocks with poor liquidity. Amihud and Mendelson (1986) and Lee and Swaminathan (2000) have documented the role of liquidity in asset pricing models. In empirical literature too, a negative relationship between returns and liquidity has been identified for several mature and emerging equity markets (Chiang & Zheng, 2015; Drew et al., 2006; Gharghori et al., 2009; Gregoriou et al., 2016). Empirical studies have found evidence of a positive relationship between profitability and returns. The studies on mature markets found that higher profitability leads to higher returns (Artmann et al., 2011; Cohen et al., 2002; Fama & French, 2008; Fitzpatrick & Ogden, 2009; Haugen & Baker, 1996; Novy-Marx, 2013). Fama and French (2008) show that profitability anomaly exists in smaller shares and find a positive relationship between the two. Aharoni et al. (2013) find evidence of a positive relationship between expected profitability and returns. For emerging markets, the evidence on the positive relationship between profitability and returns is mixed. Chen et al. (2018) in their study of 33 markets register a less significant profitability effect in emerging markets and confirm that profitability measured through quarterly updates, like earnings, is superior than annual updates in predicting returns. Foye (2018) finds evidence of significant profitability premium in Eastern Europe and Latin America but not in Asia. Leite et al. (2018) find little evidence of profitability effect in their study for 12 emerging markets. Investment effect, also called the asset growth effect, refers to the tendency of firms with high asset growth to generate lower returns in the future. Investment effect is attributed to rational factors like optimal investment effect (Watanbe et al., 2013). Other studies link investment effect with market mispricing, resulting from overinvestment by empire-building managers (Titman et al., 2004) or investors’ extrapolation of past growth rate into future periods (Cooper et al., 2008; Li & Sullivan, 2015). Watanbe et al. (2013) report stronger asset growth effect in informationally efficient markets and see asset growth effect as rational asset pricing. Investments decrease the level of risk thus bringing down the risk-adjusted returns. Later, Titman et al., 2004) lend support to the optimal investment effect hypothesis and find evidence of strong investment effect for developed financial markets but report a weak and insignificant asset growth effect for developing markets. Evidence on investment effect is also mixed. Fama and French (2008) find strong returns coming only from small firm stocks. Watanbe et al. (2013) also reports negative investment spreads for some markets. Foye (2018) finds a weak relationship between past asset growth and future returns in emerging market firms and attributes it to a strong concentration of ownership, which can gain benefits from investments for its controlling shareholders. Gonenc and Ursu (2018) study emerging markets and report that only during the 2008 financial crisis is there a significant and negative relationship between investment rates and stock returns and not for rest of the periods, especially for firms with low research intensity. Leite et al. (2018) report negative investment premiums and find limited evidence of investment effect in the 12 emerging markets they study. 3.2. Literature review—local, foreign and world factors In prior research, asset pricing tests have been performed using local as well as global factors. Financial markets are believed to be fully integrated if the assets with similar risk offer identical expected returns, irrespective of the market. However, even in highly integrated markets investors display a preference for home assets and as a result, various asset pricing models with Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 5 of 51 international factors are unable to explain domestic returns (Bekaert et al., 2002). Griffin (2002) finds domestic factor models to be superior in explaining returns and they also have lower pricing error compared to world factors. Shackman (2005) identifies a strong positive relationship between various measures of market integration and risk-adjusted excess returns because in mature markets, ease of access to less-risky bonds offers a risk premium to equity investors and vice versa in emerging markets. Bekaert et al. (2011) find that the level of segmentation has still remained significant due to non-regulatory factors like political risk and the regions stock market development. Cakici et al. (2013) find evidence of emerging market segmentation as local returns are poorly explained by USA and global factors. Chiang and Zheng (2015) find the local and foreign components of the Fama and French factors to have high explanatory power for local excess stock returns, even though magnitude is mostly higher in case of the domestic components. Fama and French (2017) test their five factor model internationally for North America, Europe, and Asia Pacific regions and find that global five-factors fail to explain the regional portfolios. Leite et al. (2018) report superior performance of local factors, compared to USA and global factors, in explaining portfolio returns. 4. Data and its sources For developing FI index, monthly USD values of MSCI indices are obtained for 47 mature and emerging markets. MSCI indices are used owing to their uniformity in construction methodology since the study involves the cross-section of world markets. 4 Some markets are excluded as their MSCI indices are unavailable for sufficiently long periods warranted by the present study. MSCI world index is used as a global market proxy. The study period is from January 1999 to December 2019. This period has been selected so that its long enough to draw reasonable interpretations and cover both upturn and downturn phases in the market cycle. The starting year has been consciously chosen to avoid structural breaks owing to Asian market crisis which had withered considerably by 1998. 5 After developing the new FI index, markets are divided into three groups based on the rankings of the developed FI index. Returns and volatility data are derived from the monthly adjusted closing prices of the MSCI indices. In the next step, the performance of market anomalies is analysed, and asset pricing tests are conducted for 25 equity markets which form part of our original sample of 47 countries. Sample markets were excluded if they did not exhibit the threshold breadth required for constructing welldiversified decile portfolios. In addition, the study of anomalies requires a certain width in the market. Finally, twenty-five markets are studied where the number of listed companies is consistently more than 250, as per WDI data, between 1999 and 2019 and for which the MSCI is also available. All stock prices used in the study are denominated in USA dollars (USD) to control currency fluctuations and homogeneity from an international investors perspective. Monthly stock prices, adjusted for splits and dividends, have been converted into percentage returns for further estimation. Dollar-denominated month-end yields on 91-day USA treasury bills are used as a risk-free proxy. Due to the thinness of data the periods of study vary between countries. This was owing to missing price observations and/or non-availability of company attributes such as market cap, priceto-book ratio, etc. which are needed for stock classification and forming our decile portfolios. Our selection procedure is inspired by Evans and Archer (1968) who advocate that a minimum of eight shares are required in a portfolio for controlling unsystematic risk. The process shall ensure that our univariate-sorted decile portfolios have less than eight securities at no point during the study period, making them reasonably diversified. The list of sample countries along with their market proxies and study periods is given in Table 1. The MSCI and market-level data have been sourced from Bloomberg. For countries where data was thin, we use Thomson Reuters Eikon (Refinitiv). Finally, we compile annual data for six company attributes. This is because portfolio revisions based on these attributes are done on an annual basis. Market capitalization is used as a proxy for size. Price-to-book value (PB) is used to measure the value effect. Momentum is calculated on past Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 6 of 51 six-month returns. The liquidity factor is created from the average of monthly trading volumes. Return on equity is used as a measure of profitability. Finally, investment is derived from the percentage change in total assets since the previous year. In our study, accounting principles are likely to impact only the profitability ratio factor derived from return on equity. While other data points like market capitalisation, price to book value, priorreturns (momentum), liquidity have standardised definitions. There exist uniform definitions for the accounting values we have used from Refinitiv, and Bloomberg. The ratios have been used to classify the companies in each country. All company data points, for a given market, have been sourced from a single platform in our country-based analysis. Table 1. Data description: country-wise market indices and data periods Country Market Index Used Time Period Australia S&P/ASX 200 2001–2019 Brazil Sao Paulo Stock Exchange IBrX Index 2004–2019 Canada S&P/TSX Composite Index 1999–2019 China Shanghai Stock Exchange Composite Index 2004–2019 Egypt EGX 30 Index 2007–2019 France CAC Index 2002–2019 Germany DAX Index 2002–2019 Hong Kong Hang Seng Index 2000–2019 India NSE 500 Index 2004–2019 Indonesia Jakarta Stock Exchange Composite Index (JCI) 2006–2019 Israel TA-125 Index 2006–2019 Italy FTSE MIB Index 2002–2019 Japan TOPIX 500 Index 2004–2019 Malaysia FTSE Bursa Malaysia 100 Index 2001–2019 Pakistan Karachi All Share Index 2003–2019 Singapore FTSE Straits Times Index (STI) 2004–2019 South Africa JSE All Share Index 2002–2019 South Korea KOSPI Index 2002–2019 Spain IBEX 35 Index 1999–2019 Sweden OMX Stockholm Benchmark Index 1999–2019 Taiwan Taiwan Stock Exchange Weighted Index 1999–2019 Thailand Stock Exchange of Thailand SET Index 2000–2019 Turkey Borsa Istanbul 100 Index 2001–2019 UK FTSE All-Share Index 1999–2019 USA S&P 500 Index 1999–2019 The table lists the sample countries for which equity market anomalies are studied along with asset pricing tests. The local stock market indices used in the study are mentioned along with data period used for each country Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 7 of 51 Table 3. (Continued) MEDIUM INTEGRATION GROUP S1 S10 S1-S10 Mean t-stat Mean t-stat Mean t-stat Italy 0.0029 (.53) 0.0018 (.36) 0.0011 (.25) Singapore .0217*** (2.71) 0.0073 (1.56) .0144** (2.39) Hong Kong .0568*** (5.32) 0.0055 (1.37) .0513*** (5.34) Brazil .0313*** (3.44) 0.0089 (1.35) .0224*** (3.21) S.Korea .0366*** (6.32) .0141*** (2.84) .0225*** (3.76) S.Africa .0328*** (4.44) .0109** (2.04) .0219*** (3.30) Taiwan .0282*** (4.31) 0.0029 (.62) .0253*** (6.20) Japan .0188*** (4.76) 0.0031 (.93) .0157*** (5.69) Indonesia .0367*** (5.78) 0.0122 (1.77) .0245*** (3.85) Mean .0295*** (5.65) .0074*** (4.76) .0221*** (4.71) LOW INTEGRATION GROUP S1 S10 S1-S10 Mean t-stat Mean t-stat Mean t-stat India .0491*** (4.87) 0.0116 (1.60) .0374*** (5.12) Thailand .0331*** (5.80) 0.0091 (1.71) .0240*** (4.50) (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 14 of 51 Table 3. (Continued) LOW INTEGRATION GROUP S1 S10 S1-S10 Mean t-stat Mean t-stat Mean t-stat China .0335*** (3.95) 0.0104 (1.55) .0231*** (3.51) Pakistan .0373*** (3.82) 0.0094 (1.69) .0279*** (2.99) Malaysia .0232*** (4.40) 0.0061 (1.74) .0171*** (4.15) Turkey 0.0162 (1.92) 0.0120 (1.44) 0.0042 (.85) Israel .0099*** (2.66) .0093*** (2.91) 0.0006 (.29) Egypt .0351** (2.57) −0.0032 (−.50) .0384*** (3.23) Mean .0297*** (6.25) .0081*** (4.34) .0216*** (4.12) For all 25 sample markets, return differentials are estimated by using corner portfolios (S1 and S10) based on market capitalization.S1 and S10 indicate the smallest and largest size-sorted decile portfolios. ** and *** indicate significance at 5% level and 1% levels, respectively Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 15 of 51 Table 4. Unadjusted returns for value-sorted deciles All Markets V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat All Markets .0231*** (11.79) .0095*** (8.35) .0136*** (8.45) HIGH INTEGRATION GROUP V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat USA .0160*** (3.43) .0119*** (3.44) 0.0041 (1.08) UK .0195*** (4.25) .0074** (2.12) .0121*** (3.92) France .0171*** (3.09) .0089*** (2.02) .0082** (2.15) Germany .0277*** (4.59) 0.0083 (1.67) .0195*** (4.32) Canada .0273*** (4.35) .0171*** (3.13) 0.0102 (1.91) Sweden .0170*** (3.27) 0.0090 (1.53) 0.0080 (1.79) Australia .0281*** (4.23) .0128** (2.24) .0153*** (3.33) Spain 0.0033 (.98) −0.0036 (−1.08) .0069** (2.45) Mean .0195*** (6.17) .0090*** (3.97) .0105*** (5.64) MEDIUM INTEGRATION GROUP V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat Italy 0.0060 (1.03) 0.0019 (.35) 0.0042 (1.09) (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 16 of 51 Table 4. (Continued) MEDIUM INTEGRATION GROUP V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat Singapore .0266*** (3.66) 0.0090 (1.66) .0176*** (3.53) Hong Kong .0299*** (3.89) .0130** (2.14) .0170*** (2.64) Brazil .0242*** (3.13) 0.0131 (1.68) 0.0111 (1.61) S.Korea .0295*** (4.84) .0188*** (3.41) .0107** (2.37) S.Africa .0326*** (5.13) .0124** (2.41) .0202*** (3.95) Taiwan .0217*** (2.79) 0.0045 (.85) .0172*** (2.84) Japan .0119*** (2.95) 0.0074 (1.90) 0.0045 (1.42) Indonesia .0375*** (4.41) .0122** (2.01) .0253*** (3.76) Mean .0244*** (6.91) .0103*** (5.67) .0142*** (5.66) LOW INTEGRATION GROUP V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat India .0431*** (3.81) .0161** (2.41) .0270*** (3.10) Thailand .0257*** (4.62) 0.0082 (1.47) .0176*** (4.26) China .0222*** (2.87) .0168** (2.27) 0.0054 (1.16) (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 17 of 51 Table 4. (Continued) LOW INTEGRATION GROUP V1 V10 V1-V10 Mean t-stat Mean t-stat Mean t-stat Pakistan .0314*** (3.73) .0116** (2.15) .0199*** (2.68) Malaysia .0174*** (3.06) 0.0053 (1.49) .0121*** (3.04) Turkey .0243*** (2.62) 0.0103 (1.19) .0140*** (2.75) Israel 0.0074 (1.73) .0079** (2.33) −0.0005 (−.23) Egypt .0289*** (2.74) −0.0029 (−.33) .0318*** (4.33) Mean .0251*** (6.35) .0092*** (3.85) .0159*** (3.96) For all 25 sample markets, return differentials are estimated by using corner portfolios (V1 and V10) based on price-to-book value. V1 and V10 indicate the smallest and largest value-sorted decile portfolios. ** and *** indicate significance at 5% level and 1% levels, respectively Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 18 of 51 The size effect is observed for all the sample markets as small firm stocks generate higher returns than big firm stocks. Table 3 illustrates that the mean monthly size premium (S1-S10) is statistically significant, at 5% level, for 21 out of 25 countries. The highest monthly size premium is observed for Hong Kong (5.13%) followed by Egypt (3.84%), India (3.74%) and Australia (3.7%). In contrast, the size premium, though positive, is small for Israel (0.06%), Italy (0.11%) and Spain (0.22%). Further, mean returns, by and large, monotonically decline as one moves from small to big stock portfolios. The monthly global size premium stands at 2.16%, which is also significant. Thus, the universality of the size effect is reconfirmed as the mean size premium is statistically significant for all the three financial integration groups as well. Size effect does not seem to be impacted much by financial integration settings as the average premium is strong and almost similar across our integration groups. Table 4 illustrates that the value premium (V1-V10) is positive for all markets except Israel. However, only 17 out of 25 markets exhibit a statistically significant value effect. High and significant value premiums are observed for Egypt (3.18%), India (2.70%), Indonesia (2.53%) and South Africa (2.02%). Israel reports the smallest value premium (−0.05%). The global monthly value premium is 1.36% which is also statistically significant. Globally, the value effect is comparatively weaker and provides a premium which is 63% of the size premium. The value effect becomes more robust as one moves from HIGs to LIGs. Further, the value effect is comparatively weaker than the size effect for HIG vis-a-vis LIG. It may be noted that the value premium is about 50% and 74% of the size premium for HIG and LIG. Evidence on the momentum effect is mixed in the sample markets. Table 5 illustrates that nine out of twenty-five countries stocks’ register negative momentum premiums (M10-M1). The mean monthly global momentum premium is 0.22% which is not statistically significant. Significant momentum premiums are reported only in 4 out of 25 markets, namely, Australia (1.62%), Germany (1.42%), France (1.3%) and Thailand (1.14%). Thus the momentum anomaly seems to have faded over time for the majority of the world markets. Momentum premium is more pronounced and significant in the HIG markets and is recorded as 0.71% per month. On the other hand, five out of eight LIG markets exhibit price reversals, and the mean monthly premium is −0.13%. The prior return patterns seem to vary for different financial integration settings as momentum is observable for HIG while mild contrarian behaviour is noticed in LIG markets. One possible reason for such price reversals could be that low-integrated markets may have higher proportion of volatile stocks, which can weaken the profitability of momentum-sorted portfolios (Lin et al., 2020). Another plausible explanation could be that, behaviourally, market participants in less integrated markets may be more prone to overreaction to bad news which results in a contrarian effect while participants in highly integrated markets could perhaps be more disposed towards underreaction to good news thus resulting in momentum effect (See Barberis et al., 1998; Chan et al. 1996). However, causes for differences in prior returns effect need further exploration. The liquidity effect is visible across several sample markets as less liquid firms generate higher returns in most markets, consistent with Lee and Swaminathan (2000). Table 6 illustrates that the mean monthly global liquidity premium (L1-L10) is 58% and significant. A positive liquidity premium is observed for 20 sample countries, out of which it is significant only for seven markets. High monthly liquidity premiums are observed for Canada (2.44%), followed by India (2.36%) and France (1.47%). As in the case of the size effect, liquidity premiums do not differ much across our financial integration groups. Thus the liquidity anomaly doesnt seem to be highly pervasive and also not sensitive to the level of market integration. Table 7 illustrates that positive profitability premiums are observed in 16 sample markets where highly profitable firms outperform weakly profitable firms, consistent with Fama and French (2008). Premiums for 6 (Pakistan, Thailand, Italy, Indonesia, Spain and France) of these 16 markets Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 19 of 51 Table 5. Unadjusted Returns for Prior returns-sorted Deciles All Markets M1 M10 M10-M1 Mean t-stat Mean t-stat Mean t-stat All Markets .0161*** (8.72) .0183*** (9.99) .0022 (1.48) HIGH INTEGRATION GROUP M1 M10 M10-M1 Mean t-stat Mean t-stat Mean t-stat USA .0164*** (3.11) .0200*** (4.36) 0.0036 (.67) UK 0.0102 (1.82) .0141*** (3.47) 0.0038 (.88) France 0.0080 (1.29) .0213*** (4.48) .0133*** (2.77) Germany .0141** (2.34) .0283*** (5.81) .0142*** (3.14) Canada .0281*** (4.18) .0259*** (4.24) −0.0023 (−.40) Sweden 0.0133 (1.75) .0157*** (2.92) 0.0024 (.39) Australia .0194** (2.55) .0356*** (5.14) .0162*** (2.82) Spain 0.0002 (.04) 0.0061 (1.53) 0.0059 (1.49) Mean .0137*** (4.41) .0209*** (6.03) .0071*** (2.86) MEDIUM INTEGRATION GROUP M1 M10 M10-M1 Mean t-stat Mean t-stat Mean t-stat Italy 0.0018 (.28) 0.0065 (1.37) 0.0047 (.90) Singapore 0.0111 (1.37) .0144** (2.28) 0.0034 (.58) Hong Kong .0185** (2.49) .0211*** (2.78) 0.0026 (.40) Brazil .0184** (1.99) .0268*** (3.15) 0.0084 (1.10) S.Korea .0389*** (5.06) .0275*** (3.09) −0.0114 (−1.37) S.Africa .0222*** (3.60) .0311*** (4.43) 0.0089 (1.37) Taiwan 0.0131 (1.79) 0.0122 (1.92) −0.0009 (−.16) Japan .0102** (2.33) .0110** (2.51) 0.0008 (.19) Indonesia .0292*** (3.08) .0207*** (3.13) −0.0085 (−1.13) Mean .0181*** (4.64) .0190*** (6.35) 0.0009 (.36) LOW INTEGRATION GROUP M1 M10 M10-M1 Mean t-stat Mean t-stat Mean t-stat India .0278*** (2.75) .0280*** (3.68) 0.0002 (.03) Thailand 0.0107 (1.57) .0221*** (3.46) .0114** (2.23) China .0171** (2.14) .0151** (2.00) −0.0019 (−.41) Pakistan .0280*** (3.37) .0253*** (3.42) −0.0026 (−.33) Malaysia 0.0085 (1.55) .0115** (2.51) 0.0030 (.84) Turkey 0.0160 (1.77) 0.0081 (.94) −0.0079 (−1.63) (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 20 of 51 are statistically significant. The mean monthly global profitability premium is positive and significant at 0.39%. Nine markets exhibit small negative profitability premiums. This difference from Novy-Marx (2013) could be due to the use of gross profits as a measure of profitability and inclusion of only non-financial firms in their study sample while we use return-on-equity measure and also include the non-financial firms. Mean profitability premiums rise sharply from 0.08% to 0.66% as one moves from HIG to LIG markets. Thus, the profitability effect seems to be more pronounced for low-integrated markets. Geographically it is interesting to observe that LIG Asian economies generally exhibit profitability premiums while most MIG Asian economies report negative premiums. Further, all European economies, which are highly integrated, show positive premiums. In contrast to European markets, highly integrated countries of USA, Canada and Australia exhibit a negative profitability premium. The cross-sectional patterns in profitability premia need further attention in future research. Except for Israel and Malaysia, other less integrated market investors seem to reward higher profitability stocks with higher returns. We see a clear distinction between European and nonEuropean HIG markets in the case of profitability premium. All European markets have positive profitability premiums, while non-European markets like the USA, Canada and Australia show negative profitability premiums for our sample stocks over the last two decades. Table 8 illustrates that the investment effect, also called the asset growth effect, is found to be positive for nine markets, which is consistent with Fama & French, 2015) contention that low investment (conservative) firms outperform high investment (aggressive) firms. Only the USA out of these nine markets shows a significant investment effect. Majority of the markets, 16 out of 25, experience negative investment premium, 5 of which are statistically significant. The mean monthly global investment premium is negative (−0.26%) and statistically significant, thus implying aggressive stocks outperform conservative stocks. Interestingly, all European economies exhibit negative investment premiums. The net investment premiums are small and negative for all financial integration groups with little difference for HIG and LIG. Just like Foye (2018) and Gonenc and Ursu (2018), we too find that the asset-growth effect is mixed among our sample markets. One possible explanation for the positive relationship between asset growth and returns in various sample markets could be the idiosyncratic financing choices determined by institutional factors. In several markets, including EU and other emerging economies; bank financing is the dominant mode of fundraising (See Astrauskaite & Paškevicius, 2014; Langfield & Pagano, 2015), and it helps reduce agency costs associated with overinvestment through enhanced financial supervision (Harvey et al., 2004). Banks have better access to private information than bondholders in capital markets, who are more reliant on publicly available information (Fama, 1985). Banks have higher incentives to undertake information acquisition as they have large stakes in borrower funding LOW INTEGRATION GROUP M1 M10 M10-M1 Mean t-stat Mean t-stat Mean t-stat Israel .0126** (2.04) 0.0079 (1.92) −0.0047 (−.80) Egypt 0.0088 (.79) 0.0014 (.13) −0.0075 (−.81) Mean .0162*** (5.46) .0149*** (4.18) −0.0013 (−.52) For all 25 sample markets, return differentials are estimated by using corner portfolios (M1 and M10) based on 6-month prior returns. M1 and M10 indicate the smallest and largest prior returns-sorted decile portfolios. ** and *** indicate significance at 5% level and 1% levels, respectively Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 21 of 51 (Boot et al., 1993). The empirical evidence on investment anomaly seems weak and tilted towards a negative investment premium. However, the factors leading to marginally superior returns in high asset growth firms from many sample markets require further examination. To sum up the study of average monthly unadjusted returns, we find that size and value effect are the dominant effects and offer the highest returns. Size premium, at 2.16% per month, is highest among the six anomalies analysed across all sample markets, followed by the value premium at 1.35% p.m. The momentum effect weans out at low levels of integration, suggesting that momentum strategy is better suited for HIG markets. A statistically significant liquidity premium is observed only in MIG markets. The profitability effect is more visible in the less integrated markets, and the investment effect is not observed in either of the integration groups. 7 We try to explain these anomaly premium patterns across financial integration groups through prior literature. It is observed that size and liquidity premia are quite similar across all three integration groups (Table 9). Small size and low liquidity firms are generally neglected and have relatively lower coverage by analysts from investment advisory companies. The stocks with poor analyst coverage tend to have higher transaction costs and lower liquidity (Dang et al., 2019). As these phenomena are pretty universal in nature we observe similar size and value premia across all integration groups. In case of other anomalies like value (price-to-book value) and profitability (return on equity), the reaction of investors to new accounting-based information could be different in HIG and LIG markets. Many LIG markets are also emerging markets, which are more sentiment-driven and investors may be prone to an overreaction (Ahmad & Hussain, 2001; Tripathi & Gupta, 2009; Wu, 2011) to accounting-based information leading to higher premiums, unlike the more mature markets (Clare & Thomas, 1995). The global mean monthly returns on six market anomalies are shown in Figure 1. The size effect is dominant in the world markets, followed by the value and liquidity effects. The momentum, profitability and asset growth anomalies are weak for global markets. Further small firms, low price-to-book value and less liquid stocks outperform big firms, high price-to-book value firms for most of the sample markets. Momentum patterns are observed for HIG markets, while most LIG markets exhibit weak contrarian behaviour. The profitability effect is more pronounced in LIG markets. The evidence on asset-growth anomaly is mixed, and mildly negative premiums are observed across all financial integration-based market groups. Figure 2 illustrates mean monthly premiums for the six market anomalies across different financial integration groups. More financially integrated economies tend to provide lower value and profitability premiums than less integrated markets. Momentum patterns are stronger for more integrated markets. Size, liquidity and investment premiums do not vary much across varying financial integration settings. Mean monthly return differentials on characteristic-sorted corner portfolios for all 25 sample markets and their significance is presented as a heat map in Figure 3. It contains the performance of equity market anomalies across the sample countries. France reports the most significant anomalies, i.e. 5 out of 6, the only exception being the investment effect. Five markets i.e. Australia, UK, Thailand, Pakistan and Indonesia, exhibit four significant anomalies. Size, profitability, and investment effects are significant for the US market. No significant anomaly is observed for Israel, while only the size effect seems strong in the case of Brazil. The heat map provides vital information to global investors regarding making market choices for designing anomaly based trading strategies in different markets. More integrated markets report a higher number of significant anomalies (25 out of 48) compared to less integrated markets (18 out of 48). A part of this result may be explained by the fact that some of the low-integrated economies have high market risk, and they catch much lower investor attention, leading to limited and infrequent trading in many financial assets from these markets. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 22 of 51 Table 6. Unadjusted returns for liquidity-sorted deciles All Markets L1 L10 L1-L10 Mean t-stat Mean t-stat Mean t-stat All Markets .0159*** (8.84) .0101*** (9.74) .0058*** (3.67) HIGH INTEGRATION GROUP L1 L10 L1-L10 Mean t-stat Mean t-stat Mean t-stat USA .0136*** (4.49) .0128*** (3.57) 0.0007 (.28) UK .0114*** (3.20) 0.0043 (1.14) .0071*** (3.48) France .0210*** (4.75) 0.0063 (1.29) .0147*** (3.18) Germany .0148*** (3.94) 0.0098 (1.85) 0.0051 (1.17) Canada .0337*** (5.31) .0093** (2.09) .0244*** (4.22) Sweden 0.0106 (1.33) .0098** (2.07) 0.0008 (.10) Australia .0129*** (2.67) .0127** (2.55) 0.0002 (.06) Spain 0.0013 (.45) 0.0030 (.65) −0.0017 (−.41) Mean .0149*** (4.22) .0085*** (6.15) 0.0064 (1.89) MEDIUM INTEGRATION GROUP L1 L10 L1-L10 Mean t-stat Mean t-stat Mean t-stat Italy −0.0028 (−.75) 0.0020 (.39) −0.0049 (−1.25) Singapore .0176*** (3.00) 0.0042 (.64) .0135** (2.52) Hong Kong .0202*** (3.02) 0.0113 (1.87) 0.0089 (1.58) Brazil .0147*** (3.13) .0164** (2.11) −0.0017 (−.24) S.Korea .0225*** (3.86) .0212*** (3.85) 0.0014 (.32) S.Africa .0226*** (3.55) .0113** (2.12) .0114** (2.05) Taiwan .0141*** (2.75) 0.0055 (.95) .0086** (2.23) Japan .0084*** (3.15) 0.0076 (1.78) 0.0008 (.27) Indonesia .0249*** (6.06) 0.0144 (1.71) 0.0105 (1.25) Mean .0158*** (5.14) .0104*** (4.73) .0054** (2.32) LOW INTEGRATION GROUP L1 L10 L1-L10 Mean t-stat Mean t-stat Mean t-stat India .0385*** (5.06) 0.0149 (1.69) .0236*** (3.29) Thailand .0114*** (4.46) 0.0114 (1.53) 0.0000 (.00) China .0194*** (2.63) .0157** (2.25) 0.0037 (.74) Pakistan .0159*** (3.61) 0.0120 (1.65) 0.0038 (.56) Malaysia .0115*** (3.14) 0.0075 (1.46) 0.0039 (1.15) Turkey .0168** (2.24) 0.0184 (1.92) −0.0016 (−.33) (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 23 of 51 H-FF-3 factor model which has additional local and foreign Fama-French factors for size and value. The H-FF-5 factor model has local and foreign factors for profitability and investment added to the H-FF-3 factor model. Overall, the performance of hybrid models is superior to both local and world factor models. Mean goodness of fit for all markets are H-CAPM, H-F F-3 and H-FF-5 are 0.693, 0.776 and 0.795, (e) : Unadjusted Returns for Profitability-sorted Decile Portfolios 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Mean Monthly Return Profitability-sorted Portfolios High Integration Medium Integration Low Integration Figure 1. Continued. (f): Unadjusted Returns for Investment-sorted Decile Portfolios 0.0% 0.5% 1.0% 1.5% 2.0% I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 Mean Monthly Return Investment-sorted Portfolios High Integration Medium Integration Low Integration Table 9. Mean monthly return differentials on characteristic-sorted corner portfolios Size (S1-S10) Value (V1-V10) Momentum (M10-M1) Liquidity (L1-L10) Profitability (P10-P1) Investment (I1-I10) All Markets 0.0216*** 0.0135*** 0.0022 0.0058*** 0.0039** −0.0026** (t-stat) (8.73) (8.45) (1.48) (3.67) (2.12) (−2.11) HIG (t-stat) 0.0212*** 0.0105*** 0.0071** 0.0064 0.0008 −0.0022 (5.29) (5.64) (2.86) (1.89) (0.22) (−1.43) MIG (t-stat) 0.0221*** 0.0142*** 0.0009 0.0054** 0.0044 −0.0036 (4.71) (5.66) (0.36) (2.32) (1.61) (−1.43) LIG (t-stat) 0.0216*** 0.0159*** −0.0013 0.0055 0.0066 −0.002 (4.12) (3.96) (−0.52) (1.72) (1.74) (−0.72) Panel A contains return differentials that are estimated by using corner portfolios (decile one and decile ten) based on each company characteristic. For size premium, we calculate the difference between small (S1) and big firm (S10) stock returns. In the case of the value effect, we take the difference between low (V1) and high PB stocks (V10). For prior returns, past losers (M1) are subtracted from past winners (M10). In the case of momentum (M10-M1) exhibit a positive sign while a negative sign implies price reversals. Similarly, liquidity premium is the difference between low liquidity (L1) and high liquidity (L10) stocks, while profitability effect is the difference between high profitable (P10) and low profitable (P1) firms. Investment premium is estimated as the difference between low investment (I1) and high investment (I10) companies. ** and *** indicate significance at 5% level and 1% levels, respectively. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 30 of 51 respectively, which are higher than counterpart local and world factor models. The FF foreign factors add a 1.3% additional variance of asset returns compared to FF-5 local factors. We find that hybrid, H-FF-5, model performs better than all the competing models across the three integration groups. As expected, foreign factors do the best job for highly integrated economies. The foreign factors provide an additional explanation of asset returns to the tune of 1.9%, 1.5% and 0.5% for HIG, MIG and LIG. Putting it all together, H-FF-5 seems to be the most suitable descriptor of asset pricing for high and medium integrated markets. For low-integrated markets, the contribution of foreign factors is marginal. Since the contribution of foreign factors is marginal, one can employ the L-FF-5 model as the performance benchmark for LIG markets, owing to its parsimonious factor structure. After adjusting for degrees of freedom, the additional foreign factors incrementally explain domestic returns by about 1%. However, the superior performance of hybrid models vis-à-vis local factor models varies considerably across integration groups. The highest incremental explanation by foreign factors is registered in the case of MIG and HIG markets, while it is the least for LIG markets. Model-wise too, the highest incremental explanation of almost 2% is recorded from local FF-5 to hybrid FF-5 model in HIG markets. This is along expected lines as foreign factors do not contribute much in explaining returns for LIG markets. So we find H-FF-5 factor model to be the most suitable model for HIG and MIG markets, while the local FF-5 model seems adequate for LIG. The absolute values of mean alphas are reported for one-factor CAPM and multifactor models (See Table 12–14). We observe that alphas are lower for multifactor models when compared to alphas for one-factor CAPM. The alphas lower when we use local or hybrid factor models as compared to those of world factor models and thus confirm the efficacy of local and hybrid factor Table 10. Testing for significance in risk and return (1) (2) (3) (4) (5) Integration Groups Return Mean t-test p-value Return Volatility F-test p-value Size HIG 0.0212 0.893 0.0377 0.129 LIG 0.0216 0.0418 Value HIG 0.0159 0.041** 0.0376 0.990 LIG 0.0158 0.0375 Momentum HIG 0.0013 0.069* 0.0503 0.108 LIG 0.0000 0.0451 Liquidity HIG 0.0055 0.655 0.0352 0.000*** LIG 0.0039 0.0525 Profitability HIG 0.0066 0.096* 0.0366 0.128 LIG 0.0059 0.0406 Investment HIG −0.0020 0.651 0.0235 0.000*** LIG −0.0027 0.0405 Mean monthly return differentials on characteristic-sorted corner portfolios for high, medium and low integration group markets are estimated from corner portfolios (decile one and decile ten) for high and low integration group markets. The premium series is created by assigning equal weights to each market. We apply t-test to check for significant differences in mean return series of high and low integration markets. Similarly, to test for differences in risk, estimated by standard deviation, we apply F-test. *, ** and *** indicate significance at 10%, 5% level and 1% levels, respectively. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 31 of 51 models in explaining the variance in portfolio returns. Within integration groups, the mean absolute alpha values for HIG markets are comparatively smaller than those of LIG markets. This is observed for all three types of factor models-local (Table 12), world (Table 13), and hybrid (Table 14). These low alphas imply smaller mispricing errors and hence confirm the predictive superiority of multifactor models. This also confirms lower mispricing errors in multifactor models. 7. Robustness tests We perform robustness tests to confirm that our results are not an outcome of specific estimation procedures. We redevelop the financial integration index using forty-month, instead of the thirtymonth, rolling window of returns and conditional volatility. We observe no change in the classification of the HIG, MIG, and LIG markets. (a) (b) (d) (c) (e) (f) 2.12% 2.21% 2.16% 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% HIG MIG LIG Mean Monthly Return Size Premium (S1-S10) 1.05% 1.42% 1.59% 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% HIG MIG LIG Mean Monthly Return Value Premium (V1-V10) 0.71% 0.09% -0.13% -0.25% 0.25% 0.75% HIG MIG LIG Mean Monthly Return Momentum Premium (M10-M1) 0.64% 0.54% 0.55% 0.00% 0.25% 0.50% 0.75% HIG MIG LIG Mean Monthly Returns Liquidity Premium (L1-L10) 0.08% 0.44% 0.66% 0.00% 0.25% 0.50% 0.75% HIG MIG LIG Mean Monthly Returns Profitability Premium (P10-P1) -0.22% -0.36% -0.20% -0.40% -0.15% 0.10% HIG MIG LIG Mean Monthly Returns Investment Premium (I1-I10) Figure 2. Return differentials on decile portfolios in three financial integration groups. Note: The figures indicate the mean monthly return differentials on characteristic-sorted corner portfolios for high, medium and low integration group markets. HIG, MIG and LIG represent high, medium and low integration group of markets, respectively. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 32 of 51 We constructed decile portfolios in the main study. As a robustness check, we also construct quintile portfolios to evaluate if our anomaly based returns are sensitive to alternative portfolio formation procedures. We did not find evidence of significant differences in anomaly premiums for quintile and decile portfolio formations. Hence our results are robust for portfolio construction procedures as illustrated in Appendix III table. We also reconstruct our world and foreign factors using equal-weights instead of value-weights. Asset pricing tests are repeated using equally weighted versions of world factor models. We also test hybrid models involving equally weighted foreign factors. The results based on equally weighted factor models are similar to those for valueweighted factor models, reported earlier in the study. These findings are consistent with Griffin (2002). Thus, our asset pricing results are robust for alternative factor-weighing procedures. 8 8. Conclusion In this study, we focus on the performance of key equity market anomalies and evaluate the ability of alternative asset pricing benchmarks’ ability to explain such anomalies under different financial integration settings. We find that size is the most dominant anomaly in world markets followed by value and liquidity. Value and profitability effects are stronger for less integrated markets. Highly integrated High Integration Group S1-S10 V1-V10 M10-M1 L1-L10 P10-P1 I1-I10 USA *(+) *(-) *(+) UK *(+) *(+) *(+) *(-) France *(+) *(+) *(+) *(+) *(+) Germany *(+) *(+) *(+) Canada *(+) *(+) *(-) Sweden *(+) Australia *(+) *(+) *(+) *(-) Spain *(+) *(+) Medium Integration Group S1-S10 V1-V10 M10-M1 L1-L10 P10-P1 I1-I10 Italy *(+) *(-) Singapore *(+) *(+) *(+) Hong Kong *(+) *(+) Brazil *(+) S.Korea *(+) *(+) S.Africa *(+) *(+) *(+) Taiwan *(+) *(+) *(+) Japan *(+) Indonesia *(+) *(+) *(+) *(-) Low Integration Group S1-S10 V1-V10 M10-M1 L1-L10 P10-P1 I1-I10 India *(+) *(+) *(+) Thailand *(+) *(+) *(+) *(+) China *(+) Pakistan *(+) *(+) *(+) *(-) Malaysia *(+) *(+) Turkey *(+) *(-) Israel Egypt *(+) *(+) Figure 3. Return differentials on market anomalies for sample countries. Note: For size premium, we calculate the difference between small (S1) and big firm (S10) stock returns. In the case of the value effect, we take the difference between low (V1) and high PB stocks (V10). For prior returns, past losers (M1) are subtracted from past winners (M10). Similarly, liquidity premium is the difference between low liquidity (L1) and high liquidity (L10) stocks, while profitability effect is the difference between high profitable (P10) and low profitable (P1) firms. Finally, the investment premium is estimated as the difference between low investment (I1) and high investment (I10) companies.* (+) values denote that return differentials are positive and significant at 5% level. *(-) values imply that return differ entials are negative and statistically significant at 5% level Blank represents return differential values which are not statistically significant Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 33 of 51 Table 11. Correlation between characteristic and return premiums PANEL A HIGH INTEGRATION GROUP Size Value Momentum Liquidity Profitability Investment USA 4.17 7.68 0.13 4.13 61.11 0.80 UK 5.63 6.63 0.13 6.59 65.11 0.92 France 6.47 5.65 0.14 10.88 56.41 0.82 Germany 7.40 5.46 0.17 9.97 64.23 0.87 Canada 5.90 5.32 0.21 6.81 70.00 1.21 Sweden 7.32 6.77 0.21 8.43 92.74 1.21 Australia 7.32 7.37 0.24 6.96 87.77 1.31 Spain 8.46 6.52 0.14 11.41 70.96 1.01 MEDIUM INTEGRATION GROUP Size Value Momentum Liquidity Profitability Investment Italy 7.09 5.14 0.16 9.27 68.22 0.87 Singapore 6.17 4.36 0.24 7.39 65.04 1.01 Hong Kong 6.69 6.00 0.24 6.20 82.97 1.27 Brazil 11.49 6.46 0.17 13.16 84.83 1.05 S.Korea 5.60 3.89 0.12 6.75 58.40 0.81 S.Africa 8.39 6.16 0.26 8.96 79.21 1.12 Taiwan 4.79 4.23 0.23 5.30 46.97 0.76 Japan 3.82 3.77 0.22 5.09 31.39 0.42 Indonesia 6.66 5.88 0.17 11.17 65.10 0.89 (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 34 of 51 Table 11. (Continued) LOW INTEGRATION GROUP Size Value Momentum Liquidity Profitability Investment India 5.20 8.09 0.23 6.90 62.85 0.95 Thailand 5.67 4.72 0.22 10.32 63.91 0.78 China 4.64 6.46 0.17 3.77 43.45 0.97 Pakistan 8.62 5.70 0.28 10.73 73.43 0.86 Malaysia 5.70 4.00 0.16 6.48 53.59 0.77 Turkey 6.77 4.61 0.21 7.71 77.38 1.04 Israel 3.83 7.67 0.11 3.80 81.98 1.02 Egypt 6.33 5.59 0.28 8.89 64.26 0.81 PANEL B Size Value Momentum Liquidity Profitability Investment All Country 0.02 −0.05 0.22 0.03 0.21 0.02 Panel A includes the absolute mean characteristic differences of corner portfolios. The characteristic differences are calculated for corner portfolios (decile one and decile ten). For size and volume log values have been taken. So, the characteristic premium for price-to-book (PB) value is the absolute difference between average PB for decile one (V1) and decile ten (V10) companies. Panel B shows association between the correlations between absolute values of characteristic differences and absolute return premiums. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 35 of 51 Table 12. Goodness-of-fit of alternative asset pricing benchmarks using local factors ALL MARKETS L-CAPM L-FF-3 L-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 All Markets 0.007 0.685 0.004 0.765 0.004 0.782 HIGH INTEGRATION GROUP L-CAPM L-FF-3 L-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 USA 0.008 0.738 0.002 0.837 0.002 0.859 UK 0.008 0.767 0.002 0.860 0.001 0.870 France 0.009 0.711 0.006 0.769 0.006 0.781 Germany 0.007 0.682 0.003 0.758 0.002 0.774 Canada 0.009 0.681 0.004 0.759 0.004 0.770 Sweden 0.006 0.629 0.003 0.720 0.004 0.745 Australia 0.011 0.752 0.004 0.817 0.004 0.830 Spain 0.003 0.560 0.002 0.606 0.003 0.642 Mean 0.007 0.690 0.003 0.766 0.003 0.784 MEDIUM INTEGRATION GROUP L-CAPM L-FF-3 L-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 Italy 0.004 0.726 0.003 0.788 0.003 0.798 Singapore 0.004 0.699 0.004 0.798 0.004 0.816 Hong Kong 0.011 0.562 0.003 0.704 0.002 0.716 (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 36 of 51 Table 12. (Continued) MEDIUM INTEGRATION GROUP L-CAPM L-FF-3 L-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 Brazil 0.005 0.678 0.003 0.740 0.003 0.754 S.Korea 0.015 0.667 0.011 0.707 0.011 0.724 S.Africa 0.008 0.634 0.005 0.686 0.004 0.707 Taiwan 0.006 0.792 0.003 0.891 0.003 0.898 Japan 0.005 0.820 0.002 0.883 0.002 0.891 Indonesia 0.010 0.632 0.004 0.718 0.003 0.730 Mean 0.008 0.690 0.004 0.768 0.004 0.782 LOW INTEGRATION GROUP L-CAPM L-FF-3 L-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 India 0.010 0.823 0.006 0.861 0.007 0.887 Thailand 0.008 0.659 0.003 0.744 0.003 0.772 China 0.010 0.738 0.002 0.863 0.002 0.866 Pakistan 0.007 0.577 0.004 0.646 0.005 0.673 Malaysia 0.004 0.677 0.003 0.802 0.002 0.818 Turkey 0.006 0.825 0.005 0.873 0.006 0.880 Israel 0.005 0.596 0.006 0.657 0.005 0.695 Egypt 0.007 0.506 0.008 0.640 0.006 0.664 Mean 0.007 0.675 0.005 0.761 0.005 0.782 Three local factor models are used to explain the cross-section of portfolio returns, namely, local CAPM (L-CAPM), local Fama-French three-factor model (L-FF-3) and local Fama-French five-factor model (L-FF-5). The goodness of fit of these alternative asset pricing models is verified by comparing their mean adj-R 2 . Models with higher mean adj-R 2 provide a better explanation of the cross-section of returns. The mean absolute alpha values have also been reported for these models. Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 37 of 51 Table 13. Goodness-of-fit of alternative asset pricing benchmarks using world factors All Markets W-CAPM W-FF-3 W-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 All Markets 0.010 0.422 0.006 0.444 0.006 0.452 HIGH INTEGRATION GROUP W-CAPM W-FF-3 W-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 USA 0.008 0.671 0.003 0.722 0.004 0.739 UK 0.006 0.648 0.004 0.705 0.004 0.707 France 0.007 0.619 0.003 0.641 0.004 0.648 Germany 0.008 0.639 0.003 0.651 0.003 0.654 Canada 0.011 0.503 0.003 0.570 0.003 0.579 Sweden 0.008 0.513 0.005 0.557 0.003 0.566 Australia 0.012 0.601 0.004 0.619 0.004 0.624 Spain 0.002 0.387 0.005 0.408 0.007 0.415 Mean 0.008 0.573 0.004 0.609 0.004 0.616 MEDIUM INTEGRATION GROUP W-CAPM W-FF-3 W-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 Italy 0.003 0.553 0.006 0.562 0.007 0.562 Singapore 0.004 0.556 0.005 0.567 0.009 0.579 (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 38 of 51 Table 13. (Continued) MEDIUM INTEGRATION GROUP W-CAPM W-FF-3 W-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 Hong Kong 0.012 0.426 0.005 0.471 0.008 0.493 Brazil 0.009 0.407 0.006 0.425 0.007 0.427 S.Korea 0.019 0.408 0.013 0.414 0.011 0.415 S.Africa 0.013 0.395 0.009 0.397 0.007 0.400 Taiwan 0.007 0.279 0.004 0.304 0.005 0.309 Japan 0.005 0.382 0.002 0.401 0.001 0.399 Indonesia 0.016 0.348 0.009 0.364 0.007 0.369 Mean 0.010 0.417 0.006 0.434 0.007 0.439 LOW INTEGRATION GROUP W-CAPM W-FF-3 W-FF-5 α adj-R 2 α adj-R 2 α adj-R 2 India 0.016 0.428 0.011 0.427 0.005 0.436 Thailand 0.013 0.210 0.006 0.221 0.004 0.245 China 0.014 0.220 0.004 0.237 0.003 0.234 Pakistan 0.016 0.048 0.012 0.056 0.014 0.052 (Continued) Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 39 of 51 Appendix I: Equations of asset pricing tests We use different asset pricing frameworks for testing the three asset pricing models, namely, CAPM, Fama-French three-factor model (FF-3) and Fama-French five-factor model (FF-5). Sample market portfolios are tested on empirical asset pricing models. 5 different asset pricing frameworks are used for testing the three asset pricing models: (1) local factor(s) (2) value-weighted world factor(s) (3) local factors and value-weighted foreign factor(s) (4) equally weighted world factors (5) local factors and equally weighted foreign factor(s) CAPM test on domestic portfolios use local, world, and hybrid market factor models: LCAPM :Rpt  Rft¼αþβRmtRft ð Þþεt(1) WCAPM :Rpt  Rft¼αþβwWRmt  Rft ð Þþεt(2) HCAPM :Rpt  Rft¼αþβRmtRft ð ÞþβfFRmt  Rft ð Þþεt(3) where R pt —R ft = mean excess monthly domestic portfolio return R mt —R ft = local market index mean excess return WR mt —R ft = world market mean excess return (equal-weighted and value-weighted) FR mt —R ft = foreign market mean excess return (equal-weighted and value-weighted) ε t = error term at a given time “t” β = slope of the market factor representing the sensitivity of market factor β w = slope of the market factor representing the sensitivity of, equal-weighted and value-weighted, World market factors β f = slope of the market factor representing the sensitivity of, equal-weighted and value-weighted, foreign market factor α = intercept or the Αlpha The world factors and foreign factors used in this study are equal weighted or value weighted on market cap. Value-weighted factors are created using Griiffin (2002) methodology. For example world market factor is the weighted average of the local market-specific components. So WR mt Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 46 of 51 = wL t-1 R mt + wF t−1 FR mt , where wL t−1 is the market cap weight (w) of the local market (L) in all sample countries market for the previous period (t-1). wF t−1 is the fraction of the total market capitalization in the previous period attributable to foreign market capitalization. The world SMB, LMH, RWM, CMA factors are also weighted averages of their respective local factors. Fama and French (1993) three factor model additionally uses the additional “size” and “value” factors to explain the portfolio returns. Size and Value factors constructed too are local, world and hybrid in nature LFF 3:Rpt  Rft¼αþβRmtRft ð Þþs SMBt ð Þþh LMHt ð Þþεt(4) WFF 3:Rpt  Rft¼αþβwWRmt  Rft ð ÞþswWSMBt ð ÞþhwWLMHt ð Þþεt(5) HFF 3:Rpt  Rft¼αþβRmtRft ð Þþs SMBt ð Þþh LMHt ð Þ þβfFRmt  Rft ð ÞþsfFSMBt ð ÞþhfFLMHt ð Þþεt (6) where SMB t = difference between returns on small size portfolio and big size portfolio LMH t = difference between returns on low value and high value portfolios WSMB t = equal-weighted and value weighted world size factor constructed from difference between returns of small size and big size portfolios of all 25 markets WLMH t = equal-weighted and value weighted world value factor constructed from difference between returns of small value and big value portfolios of all 25 markets FSMB t = equal-weighted and value weighted foreign size factor constructed from difference between returns of small size and big size portfolios of 24 markets FLMH t = equal-weighted and value weighted foreign value factor constructed from difference between returns of small value and big value portfolios of 24 markets ε t = error term at a given time “t” s = coefficients of small minus big (SMB) factor h = coefficients of low minus high (LMH) factor s w = coefficients of world SMB factor h w = coefficients of world LMH factor Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 47 of 51 s f = coefficients of foreign SMB factors h f = coefficients of foreign LMH factors The Fama & French, 2015) five factor model frameworks used in the study are given below. This model, in addition to FF-3 factors, uses the local, world and hybrid factors for profitability and investment. LFF 5:Rpt  Rft¼αþβRmtRft ð Þþs SMBt ð Þ þh LMHt ð Þþr RMWt ð Þþc CMAt ð Þþεt (7) WFF 5:Rpt  Rft¼αþβWRmt  Rft ð ÞþswWSMBt ð Þ þhwWLMHt ð ÞþrwWRMWt ð ÞþcwWCMAt ð Þþεt (8) HFF 5:Rpt  Rft¼αþβRmtRft ð Þþs SMBt ð Þ þh LMHt ð Þþr RMWt ð Þþc CMAt ð ÞþβfFRmt  Rft ð Þ þsfFSMBt ð ÞþhfFLMHt ð ÞþrfFRMWt ð ÞþcfFCMAt ð Þþεt (9) Where RMW t = difference in returns on local portfolios with high and low profitability i.e. robust profitability minus weak profitability CMAt = difference in returns on portfolios with low and high investment, i.e. returns of firms with conservative investment minus aggressive investment firms WRMW t = equal-weighted and value weighted world profitability factor created from difference between returns of high and low profitability firms of all 25 markets WCMA t = equal-weighted and value weighted world investment factor created difference between returns of low and high investment firms of all 25 markets FRMW t = equal-weighted and value weighted foreign profitability factor created from difference between returns of high and low profitability firms of all 24 markets FCMA t = equal-weighted and value weighted foreign investment factor which is difference between returns of low and high investment firms of all 24 markets r = coefficients of robust minus weak (RMW) factor c = coefficients of conservative minus aggressive (CMA) factor r w = coefficients of world RMW factor Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 48 of 51 c w = coefficients of world CMA factor r f = coefficients of foreign RMW factor c f = coefficients of foreign CMA factor Appendix II: Testing for stationarity Table below includes the results of stationarity tests. We use the Augmented Dickey Fuller Test to confirm stationarity out our time series for benchmark indices and company share prices, for each of the 25 markets and the world market. At Level At First Difference Country Index Augmented Dickey Fuller Test statistic (Test critical values at 5% level is −3.4) Probability Augmented Dickey Fuller Test statistic Probability Australia −2.1 0.5 −13.7 0.0 Brazil −1.5 0.8 −13.1 0.0 Canada −2.2 0.5 −13.5 0.0 China −2.9 0.2 −12.9 0.0 Egypt −1.8 0.7 −13.0 0.0 France −2.1 0.5 −14.1 0.0 Germany −2.3 0.4 −13.7 0.0 Hong Kong −2.7 0.2 −13.4 0.0 India −2.6 0.3 −14.3 0.0 Indonesia −2.2 0.5 −13.2 0.0 Israel −2.1 0.5 −14.1 0.0 Italy −1.7 0.8 −13.2 0.0 Japan −1.7 0.8 −14.1 0.0 Malaysia −1.7 0.8 −13.2 0.0 Pakistan −1.8 0.7 −13.6 0.0 Singapore −2.4 0.4 −14.1 0.0 S. Africa −2.6 0.3 −15.8 0.0 S. Korea −2.5 0.3 −14.2 0.0 Spain −1.8 0.7 −13.2 0.0 Sweden −2.3 0.5 −13.7 0.0 Taiwan −2.5 0.3 −14.9 0.0 Thailand −2.8 0.2 −14.7 0.0 Turkey −2.6 0.3 −15.0 0.0 UK −2.0 0.6 −14.1 0.0 USA −0.7 1.0 −15.4 0.0 World −1.5 0.8 −14.0 0.0 Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 49 of 51 Appendix III: Testing for partition sensitivity between decile and quintile portfolios Table below includes the results from testing portfolio partition sensitivity. We conducted a t-test between the mean monthly premium time series for integration groupings, of all six anomalies, derived from decile (10) and quintile-partitioned (10) portfolios. We also measured the correlations between decile and quintile portfolios’ anomaly premium times series. Table below includes the t-test and correlation results for anomaly premiums from decile and quintile portfolios Decile and quintile-sorted portfolios HIG MIG LIG p-value Correlation p-value Correlation p-value Correlation Size 0.070 0.95 0.020 0.94 0.133 0.88 Value 0.399 0.95 0.480 0.94 0.263 0.91 Momentum 0.511 0.96 0.806 0.95 0.811 0.94 Liquidity 0.378 0.95 0.897 0.91 0.859 0.96 Profitability 0.981 0.93 0.684 0.93 0.546 0.88 Investment 0.551 0.88 0.910 0.93 0.910 0.88 Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 50 of 51 © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. Cogent Economics & Finance (ISSN: 2332-2039) is published by Cogent OA, part of Taylor & Francis Group. Publishing with Cogent OA ensures: • Immediate, universal access to your article on publication • High visibility and discoverability via the Cogent OA website as well as Taylor & Francis Online • Download and citation statistics for your article • Rapid online publication • Input from, and dialog with, expert editors and editorial boards • Retention of full copyright of your article • Guaranteed legacy preservation of your article • Discounts and waivers for authors in developing regions Submit your manuscript to a Cogent OA journal at www.CogentOA.com Sharma et al., Cogent Economics & Finance (2022), 10: 2111802 https://doi.org/10.1080/23322039.2022.2111802 Page 51 of 51